What are the risks when encounter a wild animal when camping?

Yes, there is always a risk. You mitigate those risks by your behavior, and, since you didn't mention what behavioral steps you took/take, then it's difficult to answer your questions. You also didn't mention where you camp, although you did mention you were in France. But you can camp all over the world, and each place carries unique dangers that other places need not worry about.

When you have already encountered the animal, it also depends on who found whom first: if you found the animal first, you run the risk of startling it, which, depending on the animal, its state, and its environment, may run away or attack.

Snakes

Most snakes will see you as a threat and will attempt retreat. If not possible, or they are startled, you may get bitten. Of course, what happens after this depends much on the snake being venomous or not.

Small dinosaurs

Any Floridian and Australian will tell you to watch out for alligators and crocodiles. Encounters with these animals almost never end well, no matter who encounters whom. If you think casual campers need not worry, just remember that an alligator recently killed a young child in Disney World's Grand Floridian hotel. And golfers there commonly see these on the courses.

Lazy lizards

Most lizards and reptiles are harmless, insofar as being bitten (snapping turtles are a dangerous exception). But many are carriers of disease, like salmonella. And many are protected.

Bears

Black bears typically range from friendly to shy, and baby cubs will often scout out human contact, creating a logistics nightmare for mom. However, it's not uncommon for bear families to be friendly and playful, if annoying, to their human "hosts". If the bears are hungry or agitated from a previous encounter, they may become aggressive. If the bears are not used to human contact, they can become extremely dangerous. Grizzly bears are always dangerous, your danger here is you will likely be attacked by these kinds.

Skunks

If you startle or anger a skunk, you will not be allowed to ride home with your camping companions for the next decade.

Other small animals (groundhog, possum, racoons, rabbits, etc)

Not to worry. Except your food stores. Risks here are stolen food, and destruction of property in their attempts to get at said food. Raccoons in particular are very adept at stealing.

One small animal you must not touch is armadillos: they are common and friendly, but they can carry leprosy.

Big game (deer, moose, elk, etc)

Watch out. During mating season, they're extremely territorial, and moose in particular, will not think twice about charging at you. In addition, it's not uncommon for them to fight over females; in this case, one may chase the other, or they engage each other where your campsite happens to be. Your risks here can be anywhere from having your things stomped upon, them getting entangled in tarps, hammocks, tents, and tent lines, and you getting stomped on.

When not in mating season, you have less to worry about, except for moose and elk. They're still dangerous and you can be charged at.

Swine

Wild swine are not normally a threat, unless you happen upon a lair with piglets. Then, the mother will become territorial and may attack. In this case, they can be very dangerous - and fast.

Fox

They are rarely a threat, your biggest worry is your food. They can be friendly in environments where humans frequent.

Coyotes, wolves

They are territorial, and can occasionally attack. As a rule, they tend to leave humans alone, some are even friendly. Your biggest concern is your food stores.

Bats

Bats are awesome to have: the more bats, the less bugs. They're harmless, noting the general problems with mammals I mention about, below.

Birds

Depending on where you're at, falcon, eagles, hawks, owls, and other predator birds can be annoying, as they'll steal food. They generally avoid humans, so, if you have an unwatched steak that's sitting out in the open, it's fair game.

However, these predator birds can nevertheless be dangerous to humans.

Other birds can be dangerous to touch (eg, Blue-Capped Ifrita and Little Shrikethrush), which, because of its diet on a kind of beetle, can induce numbness not unlike poison dart frogs (another creature you ought to avoid, but, not typically found by most campers).

If you happen to be casually camping in Papua New Guinea, watch out for the Pitohui bird, it can also be lethal to the touch.

Do stay away from vultures. They won't directly harm you, they're carrion-eaters and are otherwise gentle birds. They are carriers of Really Bad Diseases, anthrax being one of them. Anthrax is a bacteria spread via spores, which come from dead animals (and for this reason, you ought not touch dead animals, either - keep on eye on the boys!)

Also depending on where you camp, very large birds like ostrich, rhea, and cassowary are very dangerous animals and will typically attack for no (obvious) reason.

Mice, Rats

Your biggest worry here are the fleas and ticks, which can introduce diseases like Lyme.

Insects

Well, these can be a problem, too, even though they're not animals. Scorpions, spiders, mosquitos, bees, and centipedes can be dangerous. Know the area you are in. Besides the venomous and stinging variety (either result can trigger anaphylaxis if you have allergies), you also have issues with malaria, lyme, zika, west nile, and others.

Speaking of disease, many animals - mammals - can be carriers of rabies and hentavirus. While your biggest concern with large game is being charged at, your biggest worry with smaller animals is disease and symbiotic pests - ticks and fleas.

Your encounter with an animal may draw the ire of something other than the animals themselves: the law. Some animals are protected, and so, if you do not take steps to avoid the animal, you may need to later take steps to avoid prosecution. Many reptiles and birds are protected.

In addition to finding animals (and the law) a concern, your other concern is hunters. It is common for hunting season and camping seasons to overlap. Good hunting and camping habits dictate that you should wear colored clothing. Otherwise, your otherwise friendly encounter with a deer may end in disaster for you - and not from the deer.

One last thing. All animals who have diseases (eg, rabies) or who are sick or injured, or who are pregnant, can exhibit unpredictable behavior. In this case, they are extremely dangerous.

So, lots to be careful about. Know your environment, know the law, and be prepared. Remember you are guest in animals' home. Act like a guest. Respect what you see, and take nothing for granted.

Are you likely to be attacked by a grunting thing outside your tent? Probably not. Gotta get up in the middle of the night to pee? Watch out and don't step on that scorpion.

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There's always going to be some risk being out wild camping with animals around but I have found that 99% of the time you will be fine! I've had everything from wild boar to hedgehogs and hedgehogs can be very loud!

Like cbeleites said unusual animal noises seem much louder during the night.

As for leaving the tent at night safely that really depends on your surroundings and the animals in the area. Depending on where you are you may want to store your food in bear canisters so you don't attract animals and take some other precautions.